reserve x, y, z for object,
  i, j, n for Nat,
  p, q, r for FinSequence,
  v for FinSequence of NAT;

theorem Th2:
  for i,j being Nat
  st elementary_tree i = elementary_tree j holds i = j
proof
  let i,j be Nat;
  assume elementary_tree i = elementary_tree j;
then  i <= j & i >= j by Th1;
  hence thesis by XXREAL_0:1;
end;
